Brain lateralization, a trait ubiquitous in vertebrates and invertebrates, refers to structural differences between the left and right sides of the brain or to the left and right sides controlling different functions or processing information in different ways. Many studies have looked into the advantages of lateralized brains and discovered that cerebral lateralization confers a fitness advantage. Enhancing cognitive ability has been proposed as one of the potential benefits of the lateralized brain, however, this has not been widely validated. In this study, we investigated the handedness of 34 subjects from four groups of Callitrichids, as well as their performance in two inhibitory control tasks (the revised A-not-B task and the cylinder task). The subjects had strong individual hand preferences, and only a few zoo-born individuals were ambidextrous. Sex and generation influence the strength of hand preference. In the cylinder task, the subjects showed differences between groups, and the performance of the second-generation was better than that of the first-generation. We found that neither the strength of hand preferences (ABS-HI) or direction of hand preferences (HI) was linked with success on the two inhibitory tasks. That is, we were unable to support the enhanced cognitive function hypothesis. We believe that individual ontogeny and the type of cognitive task have an impact on the support of this hypothesis. The advantages of lateralized brain may be reflected in tests that require multiple cognitive abilities.